TetLinearLgn.h

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//  Copyright (c) 2009 Scientific Computing and Imaging Institute,
//  University of Utah.
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///   @file    TetLinearLgn.h
///   @author  Martin Cole, Frank B. Sachse
///   @date    Dec 04 2004

#ifndef CORE_BASIS_TETLINEARLGN_H
#define CORE_BASIS_TETLINEARLGN_H 1

#include <cfloat>

#include <Core/Basis/TetElementWeights.h>
#include <Core/Basis/TetSamplingSchemes.h>
#include <Core/Basis/TriLinearLgn.h>
#include <Core/Basis/share.h>

namespace SCIRun {
namespace Core {
namespace Basis {

/// Class for describing unit geometry of TetLinearLgn 
class TetLinearLgnUnitElement {
public:
  /// Parametric coordinates of vertices of unit edge
  static SCISHARE double unit_vertices[4][3];
  /// References to vertices of unit edge 
  static SCISHARE int unit_edges[6][2]; 
  /// References to vertices of unit face
  static SCISHARE int unit_faces[4][3];  
  /// Normals of unit faces
  static SCISHARE double unit_face_normals[4][3];
  /// Precalculated area of faces
  static SCISHARE double unit_face_areas[4];
  /// Center of the unit element
  static SCISHARE double unit_center[3];

  TetLinearLgnUnitElement() {}
  virtual ~TetLinearLgnUnitElement() {}
  
  /// return dimension of domain 
  static int domain_dimension() 
    { return 3; } 
 
  /// return size of the domain
  static double domain_size() 
    { return 1.0/6.0; }
  
  /// return number of vertices
  static int number_of_vertices() 
    { return 4; } 
  
  /// return number of vertices in mesh
  static int number_of_mesh_vertices() 
    { return 4; }
  
  /// return number of edges 
  static int number_of_edges() 
    { return 6; }
  
  /// return degrees of freedom 
  static int dofs() 
    { return 4; } 
  
  /// return number of vertices per face 
  static int vertices_of_face() 
    { return 3; } 
  
  /// return number of faces per cell 
  static int faces_of_cell() 
    { return 4; } 

  static inline double length(int edge)
  { ///< return length
    const double *v0 = unit_vertices[unit_edges[edge][0]];
    const double *v1 = unit_vertices[unit_edges[edge][1]];
    const double dx = v1[0] - v0[0];
    const double dy = v1[1] - v0[1];
    const double dz = v1[2] - v0[2];
    return sqrt(dx*dx+dy*dy+dz*dz);
  } 
  static double area(int face) { return unit_face_areas[face]; } ///< return area
  static double volume() { return 1./6.; } ///< return volume
};


/// Class for creating geometrical approximations of Tet meshes
class TetApprox {  
public:

  TetApprox() {}
  virtual ~TetApprox() {}
  
  /// Approximate edge for element by piecewise linear segments
  /// return: coords gives parametric coordinates of the approximation.
  /// Use interpolate with coordinates to get the world coordinates.
  template<class VECTOR>
  void approx_edge(const unsigned edge, 
                   const unsigned div_per_unit, 
                   VECTOR &coords) const
  {
    typedef typename VECTOR::value_type VECTOR2;

    coords.resize(div_per_unit + 1);

    const double *v0 = TetLinearLgnUnitElement::unit_vertices[TetLinearLgnUnitElement::unit_edges[edge][0]];
    const double *v1 = TetLinearLgnUnitElement::unit_vertices[TetLinearLgnUnitElement::unit_edges[edge][1]];

    const double &p1x = v0[0];
    const double &p1y = v0[1];
    const double &p1z = v0[2];
    const double dx = v1[0] - p1x;
    const double dy = v1[1] - p1y;
    const double dz = v1[2] - p1z;

    for(unsigned int i = 0; i <= div_per_unit; i++) {
      const double d = (double)i / (double)div_per_unit;
      typename VECTOR::value_type &tmp = coords[i];
      tmp.resize(3);
      tmp[0] = static_cast<typename VECTOR2::value_type>(p1x + d * dx);
      tmp[1] = static_cast<typename VECTOR2::value_type>(p1y + d * dy);
      tmp[2] = static_cast<typename VECTOR2::value_type>(p1z + d * dz);
    }   
  }
  
  /// Approximate faces for element by piecewise linear elements
  /// return number of vertices per face
  virtual int get_approx_face_elements() const { return 3; }


  /// Approximate faces for element by piecewise linear elements
  /// return: coords gives parametric coordinates at the approximation point.
  /// Use interpolate with coordinates to get the world coordinates.
  template <class VECTOR>
  void approx_face(const unsigned face, 
                   const unsigned div_per_unit, 
                   VECTOR &coords) const
  {
    typedef typename VECTOR::value_type VECTOR2;
    typedef typename VECTOR2::value_type VECTOR3;
    
    const double *v0 = TetLinearLgnUnitElement::unit_vertices[TetLinearLgnUnitElement::unit_faces[face][0]];
    const double *v1 = TetLinearLgnUnitElement::unit_vertices[TetLinearLgnUnitElement::unit_faces[face][1]];
    const double *v2 = TetLinearLgnUnitElement::unit_vertices[TetLinearLgnUnitElement::unit_faces[face][2]];
    coords.resize(div_per_unit);
    const double d = 1. / div_per_unit;
    for(unsigned int j = 0; j<div_per_unit; j++) 
    {
      const double dj = (double)j / (double)div_per_unit;
      unsigned int e = 0;
      coords[j].resize((div_per_unit - j) * 2 + 1);
      typename VECTOR2::value_type &tmp = coords[j][e++];
      tmp.resize(3);
      tmp[0] = static_cast<typename VECTOR3::value_type>(v0[0] + dj * (v2[0] - v0[0]));
      tmp[1] = static_cast<typename VECTOR3::value_type>(v0[1] + dj * (v2[1] - v0[1]));
      tmp[2] = static_cast<typename VECTOR3::value_type>(v0[2] + dj * (v2[2] - v0[2]));

      for(unsigned int i = 0; i<div_per_unit - j; i++) 
      {
        const double di = (double)i / (double)div_per_unit;
        typename VECTOR2::value_type &tmp1 = coords[j][e++];
        tmp1.resize(3);
        tmp1[0] = static_cast<typename VECTOR3::value_type>(v0[0] + (dj + d) * (v2[0] - v0[0]) + di * (v1[0] - v0[0]));
        tmp1[1] = static_cast<typename VECTOR3::value_type>(v0[1] + (dj + d) * (v2[1] - v0[1]) + di * (v1[1] - v0[1]));
        tmp1[2] = static_cast<typename VECTOR3::value_type>(v0[2] + (dj + d) * (v2[2] - v0[2]) + di * (v1[2] - v0[2]));

        typename VECTOR2::value_type &tmp2 = coords[j][e++];
        tmp2.resize(3);
        tmp2[0] = static_cast<typename VECTOR3::value_type>(v0[0] + dj * (v2[0] - v0[0]) + (di + d) * (v1[0] - v0[0]));
        tmp2[1] = static_cast<typename VECTOR3::value_type>(v0[1] + dj * (v2[1] - v0[1]) + (di + d) * (v1[1] - v0[1]));
        tmp2[2] = static_cast<typename VECTOR3::value_type>(v0[2] + dj * (v2[2] - v0[2]) + (di + d) * (v1[2] - v0[2]));
      }
    }
  }
};

/// Class for searching of parametric coordinates related to a 
/// value in Tet meshes and fields
/// to do
template <class ElemBasis>
class TetLocate : public Dim3Locate<ElemBasis> {
public:
  typedef typename ElemBasis::value_type T;

  TetLocate() {}
  virtual ~TetLocate() {}
 
  /// find coodinate in interpolation for given value         
  template <class ElemData, class VECTOR>
  bool get_coords(const ElemBasis *pEB, VECTOR &coords, 
          const T& value, const ElemData &cd) const  
  {      
    initial_guess(pEB, value, cd, coords);
    if (this->get_iterative(pEB, coords, value, cd))
      return check_coords(coords);
    return false;
  }

protected:
  template <class VECTOR>
  inline bool check_coords(const VECTOR &x) const  
  {  
    if (x[0]>=-Dim3Locate<ElemBasis>::thresholdDist)
      if (x[1]>=-Dim3Locate<ElemBasis>::thresholdDist)
        if (x[2]>=-Dim3Locate<ElemBasis>::thresholdDist) 
          if (x[0]+x[1]+x[2]<=Dim3Locate<ElemBasis>::thresholdDist1)
            return true;

    return false;
  }
  
  /// find a reasonable initial guess 
  template <class ElemData, class VECTOR>
  void initial_guess(const ElemBasis *pElem, const T &val, const ElemData &cd, 
             VECTOR & guess) const
  {
    double dist = DBL_MAX;
    
    VECTOR coord(3);
    StackVector<T,3> derivs;
    guess.resize(3);

    const int end = 3;
    for (int x = 1; x < end; x++) 
    {
      coord[0] = x / (double) end;
      for (int y = 1; y < end; y++) 
      {
        coord[1] = y / (double) end;
        if (coord[0]+coord[1]>Dim3Locate<ElemBasis>::thresholdDist1)
          break;
        for (int z = 1; z < end; z++) 
        {
          coord[2] = z / (double) end;
          if (coord[0]+coord[1]+coord[2]>Dim3Locate<ElemBasis>::thresholdDist1)
            break;
          
          double cur_d;
          if (compare_distance(pElem->interpolate(coord, cd), 
                   val, cur_d, dist)) 
          {
            pElem->derivate(coord, cd, derivs);
            if (!check_zero(derivs)) 
            {
              dist = cur_d;
              guess = coord;
            }
          }
        }
      }
    }
  }
};



/// Class with weights and coordinates for 1nd order Gaussian integration
template <class T>
class TetGaussian1
{
public:
  static int GaussianNum;
  static T GaussianPoints[1][3];
  static T GaussianWeights[1];
};

#ifdef _WIN32
// force the instantiation of TetGaussian1<double>
template class TetGaussian1<double>;
#endif

template <class T>
int TetGaussian1<T>::GaussianNum = 1;

template <class T>
T TetGaussian1<T>::GaussianPoints[][3] = {
  {1./4., 1./4., 1./4.}};

template <class T>
T TetGaussian1<T>::GaussianWeights[] = {1.0};


/// Class with weights and coordinates for 2nd order Gaussian integration
template <class T>
class TetGaussian2 
{
public:
  static int GaussianNum;
  static T GaussianPoints[4][3];
  static T GaussianWeights[4];
};

#ifdef _WIN32
// force the instantiation of TetGaussian2<double>
template class TetGaussian2<double>;
#endif

template <class T>
int TetGaussian2<T>::GaussianNum = 4;

template <class T>
T TetGaussian2<T>::GaussianPoints[][3] = {
  {0.138196601125011,  0.138196601125011, 0.138196601125011},   
  {0.585410196624969,  0.138196601125011, 0.138196601125011},   
  {0.138196601125011,  0.585410196624969, 0.138196601125011},   
  {0.138196601125011,  0.138196601125011, 0.585410196624969}};
     
//  {1./6., 1./6., 1./6.}, {2./3., 1./6., 1./6.}, 
//  {1./6., 2./3., 1./6.}, {1./6., 1./6., 2./3.}};

template <class T>
T TetGaussian2<T>::GaussianWeights[] = {.25, .25, .25, .25};


/// Class with weights and coordinates for 3rd order Gaussian integration
template <class T>
class TetGaussian3 
{
public:
  static int GaussianNum;
  static T GaussianPoints[11][3];
  static T GaussianWeights[11];
};

template <class T>
T TetGaussian3<T>::GaussianPoints[][3] = {
  {0.2500000,  0.2500000, 0.2500000},
  {0.7857143, 0.07142857, 0.07142857},
  {0.07142857, 0.7857143, 0.07142857},
  {0.07142857, 0.07142857, 0.7857143},
  {0.07142857, 0.07142857, 0.07142857},
  {0.1005964, 0.1005964, 0.3994034},
  {0.1005964, 0.3994034, 0.1005964},
  {0.1005964, 0.3994034, 0.3994034},
  {0.3994034, 0.1005964, 0.1005964},
  {0.3994034, 0.1005964, 0.3994034},
  {0.3994034, 0.3994034, 0.1005964}};

template <class T>
T TetGaussian3<T>::GaussianWeights[] = {
  -0.01315556,
  0.007622222,
  0.007622222,
  0.007622222,
  0.007622222,
  0.02488889,
  0.02488889,
  0.02488889,
  0.02488889,
  0.02488889,
  0.02488889};

template <class T>
int TetGaussian3<T>::GaussianNum = 11;

/// Class for handling of element of type tetrahedron with 
/// linear lagrangian interpolation
template <class T>
class TetLinearLgn : 
         public BasisSimple<T>, 
         public TetApprox, 
             public TetGaussian1<double>,
         public TetSamplingSchemes, 
             public TetLinearLgnUnitElement ,
         public TetElementWeights
{
public:
  typedef T value_type;

  TetLinearLgn() {}
  virtual ~TetLinearLgn() {}

  static int polynomial_order() { return 1; }

  template<class VECTOR>
  inline void get_weights(const VECTOR& coords, double *w) const
    { get_linear_weights(coords,w); }

  template<class VECTOR>
  inline void get_derivate_weights(const VECTOR& coords, double *w) const
    { get_linear_derivate_weights(coords,w); }


  /// get value at parametric coordinate 
  template <class ElemData, class VECTOR>
  T interpolate(const VECTOR &coords, const ElemData &cd) const
  {
    double w[4];
    get_linear_weights(coords, w); 

    return (T)(w[0] * cd.node0() +
           w[1] * cd.node1() +
           w[2] * cd.node2() +
           w[3] * cd.node3());
  }
  
  /// get first derivative at parametric coordinate
  template <class ElemData,class VECTOR1, class VECTOR2>
  void derivate(const VECTOR1& /*coords*/, const ElemData &cd, 
        VECTOR2 &derivs) const
  {
    derivs.resize(3);
    
    derivs[0] = static_cast<typename VECTOR2::value_type>(-1. * cd.node0() + cd.node1());
    derivs[1] = static_cast<typename VECTOR2::value_type>(-1. * cd.node0() + cd.node2());
    derivs[2] = static_cast<typename VECTOR2::value_type>(-1. * cd.node0() + cd.node3());
  }

  /// get parametric coordinate for value within the element
  template <class ElemData, class VECTOR>
  bool get_coords(VECTOR &coords, const T& value, 
          const ElemData &cd) const  
  {
    TetLocate< TetLinearLgn<T> > CL;
    return CL.get_coords(this, coords, value, cd);
  }
 
  /// get arc length for edge
  template <class ElemData>
  double get_arc_length(const unsigned edge, const ElemData &cd) const  
  {
    return get_arc3d_length<CrvGaussian1<double> >(this, edge, cd);
  }
 
  /// get area
  template <class ElemData>
    double get_area(const unsigned face, const ElemData &cd) const  
  {
    return get_area3<TriGaussian2<double> >(this, face, cd);
  }
 
  /// get volume
  template <class ElemData>
    double get_volume(const ElemData & cd) const  
  {
    return get_volume3(this, cd);
  }


  static  const std::string type_name(int n = -1);

  virtual void io (Piostream& str);

};




template <class T>
const std::string
TetLinearLgn<T>::type_name(int n)
{
  ASSERT((n >= -1) && n <= 1);
  if (n == -1)
  {
    static const std::string name = TypeNameGenerator::make_template_id(type_name(0), type_name(1));
    return name;
  }
  else if (n == 0)
  {
    static const std::string nm("TetLinearLgn");
    return nm;
  } else {
    return find_type_name((T *)0);
  }
}




}}

template <class T>
const TypeDescription* get_type_description(Core::Basis::TetLinearLgn<T> *)
{
  static TypeDescription* td = 0;
  if(!td){
    const TypeDescription *sub = get_type_description((T*)0);
    TypeDescription::td_vec *subs = new TypeDescription::td_vec(1);
    (*subs)[0] = sub;
    td = new TypeDescription("TetLinearLgn", subs, 
      std::string(__FILE__),
      "SCIRun", 
      TypeDescription::BASIS_E);
  }
  return td;
}

const int TETLINEARLGN_VERSION = 1;
template <class T>
void
  Core::Basis::TetLinearLgn<T>::io(Piostream &stream)
{
  stream.begin_class(get_type_description(this)->get_name(),
    TETLINEARLGN_VERSION);
  stream.end_class();
}
}

#endif